3.7.16 \(\int \frac {F^{f (a+b \log (c (d+e x)^n))^2}}{(g+h x)^3} \, dx\) [616]

Optimal. Leaf size=31 \[ \text {Int}\left (\frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3},x\right ) \]

[Out]

Unintegrable(F^(f*(a+b*ln(c*(e*x+d)^n))^2)/(h*x+g)^3,x)

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Rubi [A]
time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x)^3,x]

[Out]

Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x)^3, x]

Rubi steps

\begin {align*} \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx &=\int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx\\ \end {align*}

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Mathematica [A]
time = 5.02, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x)^3,x]

[Out]

Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x)^3, x]

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Maple [A]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {F^{f \left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )^{2}}}{\left (h x +g \right )^{3}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F^(f*(a+b*ln(c*(e*x+d)^n))^2)/(h*x+g)^3,x)

[Out]

int(F^(f*(a+b*ln(c*(e*x+d)^n))^2)/(h*x+g)^3,x)

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(f*(a+b*log(c*(e*x+d)^n))^2)/(h*x+g)^3,x, algorithm="maxima")

[Out]

integrate(F^((b*log((e*x + d)^n*c) + a)^2*f)/(h*x + g)^3, x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(f*(a+b*log(c*(e*x+d)^n))^2)/(h*x+g)^3,x, algorithm="fricas")

[Out]

integral(F^(b^2*f*log((x*e + d)^n*c)^2 + 2*a*b*f*log((x*e + d)^n*c) + a^2*f)/(h^3*x^3 + 3*g*h^2*x^2 + 3*g^2*h*
x + g^3), x)

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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F**(f*(a+b*ln(c*(e*x+d)**n))**2)/(h*x+g)**3,x)

[Out]

Timed out

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(f*(a+b*log(c*(e*x+d)^n))^2)/(h*x+g)^3,x, algorithm="giac")

[Out]

integrate(F^((b*log((x*e + d)^n*c) + a)^2*f)/(h*x + g)^3, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{f\,\ln \left (F\right )\,{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^2}}{{\left (g+h\,x\right )}^3} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F^(f*(a + b*log(c*(d + e*x)^n))^2)/(g + h*x)^3,x)

[Out]

int(exp(f*log(F)*(a + b*log(c*(d + e*x)^n))^2)/(g + h*x)^3, x)

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